iterative multiuser interference reduction: turbo cdma

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1008 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 7, JULY 1999 Iterative Multiuser Interference Reduction: Turbo CDMA Paul D. Alexander, Member, IEEE, Mark C. Reed, Student Member, IEEE, John A. Asenstorfer, Member, IEEE, and Christian B. Schlegel, Senior Member, IEEE Abstract— We view the asynchronous random code-division multiple-access (CDMA) channel as a time-varying convolutional code. We study the case where the users encode their data, and, therefore, the single user transmitters and the CDMA channel appear as the concatenation of two coding systems. At the receiver we employ serial Turbo decoding strategies. Unlike conventional Turbo codes where both the inner and outer code may be selected, in our case, the inner code is due to the CDMA channel which we assume to be random. Nevertheless, the decoding system resembles the decoder of a serial Turbo code and single-user performance is obtained even for numbers of users approaching the spreading code length. Index Terms—Code-division multiple access, iterative methods, random codes, Turbo codes. I. INTRODUCTION T HE OUTPUT of a code-division multiple-access (CDMA) channel is a linear transformation of the input. In the case where the channel output noise is whitened, using the noise whitening-matched filter [1], [2], the transformed signal has some special properties. These properties enable us to view the CDMA channel as a convolutional code with the number of states being exponential in the number of users. Due to the complexity of this code, decoding schemes such as the decorrelator [3] or matched filter receivers [4] are often employed. When the users first encode their information sequences via single-user convolutional codes, the resulting system can be viewed as a concatenated coding system. Proposals that have a linear preprocessing filter to decode the inner CDMA code have been presented [5], [6]. The performance of these systems for the case where the number of users approaches the spreading code length is several decibels away from the single-user case. This loss is due to the linear decoding of the CDMA channel, which is a convolutional code in its own right. Convolutional codes are typically decoded using nonlinear techniques such as the Viterbi algorithm [7]. When the number of users is small compared to the spreading code length, a Paper approved by U. Mitra, the Editor for Spread Spectrum/Equalization for the IEEE Communications Society. Manuscript received April 1, 1997; revised October 6, 1997 and December 12, 1998. P. D. Alexander, M. C. Reed, and J. A. Asenstorfer are with the In- stitute for Telecommunications Research, University of South Australia, The Levels SA 5095, Australia (e-mail: {[email protected]; [email protected]; [email protected]). C. B. Schlegel is with the Department of Electrical Engineering, University of Utah, Salt Lake City, UT 84112 USA. Publisher Item Identifier S 0090-6778(99)05233-2. linear method is an appropriate decoder and overall system performance is satisfactory [4]–[6]. Other low complexity schemes such as a decision-feedback canceler have also been employed [8]. The maximum-likelihood solution for the asynchronous CDMA channel where the users encode their data has been formalized recently by Giallorenzi and Wilson [9]. They were able to achieve near single-user performance for the two-user case and fixed spreading codes. The decoder consisted of a Viterbi algorithm running over a trellis with a number of states that was exponential in the product of the number of users and the constraint length of the convolutional codes. Due to this complexity problem, they proposed a suboptimal technique [10]. In this paper, for large numbers of users, they were able to get within 2 dB of single-user performance. The system employed single-user decoders and there were multiple passes through each of these decoders. As will be shown, this structure is similar to the system in this paper. Recent work by Alexander et al. [11] provided a performance analysis for this system which shows the receiver achieves single-user performance for moderate . For the synchronous CDMA case, Hagenauer [12] realized that the CDMA channel could be viewed as a block code. He proposed a suboptimal scheme for decoding the CDMA channel that provided soft information in an iterative decod- ing scheme. A performance comparison with asynchronous schemes was not possible since, in the synchronous case, spreading codes may be selected according to their correlation properties. In the asynchronous case, where any possible delay profile is admitted, such explicit code design is not feasible. It is not practical to decode the CDMA channel code using full-complexity decoding techniques due to the large number of states. In this paper, we propose a suboptimal maximum a posteriori (MAP) probability technique for de- coding the CDMA channel code, and the single-user codes are decoded using full-complexity MAP probability algorithms, as described originally by Bahl et al. [13]. We make the realization that the concatenation of two convolutional codes may be decoded in a Serial Turbo Code [14] fashion at the receiver. A feature of our system is that the convolutional code corresponding to the CDMA channel has random generator polynomials. We do, however, have control over the high-level statistics of the polynomials via the spreading code length and the level of asynchronism in the channel. The exploitation of this control is not studied in this paper. 0090–6778/99$10.00 1999 IEEE

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1008 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 7, JULY 1999

Iterative Multiuser InterferenceReduction: Turbo CDMA

Paul D. Alexander,Member, IEEE,Mark C. Reed,Student Member, IEEE,John A. Asenstorfer,Member, IEEE,and Christian B. Schlegel,Senior Member, IEEE

Abstract—We view the asynchronous random code-divisionmultiple-access (CDMA) channel as a time-varying convolutionalcode. We study the case where the users encode their data, and,therefore, the single user transmitters and the CDMA channelappear as the concatenation of two coding systems. At the receiverwe employ serial Turbo decoding strategies. Unlike conventionalTurbo codes where both the inner and outer code may be selected,in our case, the inner code is due to the CDMA channel whichwe assume to be random. Nevertheless, the decoding systemresembles the decoder of a serial Turbo code and single-userperformance is obtained even for numbers of users approachingthe spreading code length.

Index Terms—Code-division multiple access, iterative methods,random codes, Turbo codes.

I. INTRODUCTION

T HE OUTPUT of a code-division multiple-access(CDMA) channel is a linear transformation of the input.

In the case where the channel output noise is whitened, usingthe noise whitening-matched filter [1], [2], the transformedsignal has some special properties. These properties enableus to view the CDMA channel as a convolutional code withthe number of states being exponential in the number ofusers. Due to the complexity of this code, decoding schemessuch as the decorrelator [3] or matched filter receivers [4]are often employed.

When the users first encode their information sequencesvia single-user convolutional codes, the resulting system canbe viewed as a concatenated coding system. Proposals thathave a linear preprocessing filter to decode the inner CDMAcode have been presented [5], [6]. The performance of thesesystems for the case where the number of users approachesthe spreading code length is several decibels away from thesingle-user case. This loss is due to the linear decoding of theCDMA channel, which is a convolutional code in its own right.Convolutional codes are typically decoded using nonlineartechniques such as the Viterbi algorithm [7]. When the numberof users is small compared to the spreading code length, a

Paper approved by U. Mitra, the Editor for Spread Spectrum/Equalizationfor the IEEE Communications Society. Manuscript received April 1, 1997;revised October 6, 1997 and December 12, 1998.

P. D. Alexander, M. C. Reed, and J. A. Asenstorfer are with the In-stitute for Telecommunications Research, University of South Australia,The Levels SA 5095, Australia (e-mail: {[email protected];[email protected]; [email protected]).

C. B. Schlegel is with the Department of Electrical Engineering, Universityof Utah, Salt Lake City, UT 84112 USA.

Publisher Item Identifier S 0090-6778(99)05233-2.

linear method is an appropriate decoder and overall systemperformance is satisfactory [4]–[6]. Other low complexityschemes such as a decision-feedback canceler have also beenemployed [8].

The maximum-likelihood solution for the asynchronousCDMA channel where the users encode their data has beenformalized recently by Giallorenzi and Wilson [9]. They wereable to achieve near single-user performance for the two-usercase and fixed spreading codes. The decoder consisted of aViterbi algorithm running over a trellis with a number ofstates that was exponential in the product of the number ofusers and the constraint length of the convolutional codes.Due to this complexity problem, they proposed a suboptimaltechnique [10]. In this paper, for large numbers of users, theywere able to get within 2 dB of single-user performance. Thesystem employed single-user decoders and there were multiplepasses through each of these decoders. As will be shown,this structure is similar to the system in this paper. Recentwork by Alexanderet al. [11] provided a performance analysisfor this system which shows the receiver achieves single-userperformance for moderate .

For the synchronous CDMA case, Hagenauer [12] realizedthat the CDMA channel could be viewed as a block code.He proposed a suboptimal scheme for decoding the CDMAchannel that provided soft information in an iterative decod-ing scheme. A performance comparison with asynchronousschemes was not possible since, in the synchronous case,spreading codes may be selected according to their correlationproperties. In the asynchronous case, where any possible delayprofile is admitted, such explicit code design is not feasible.

It is not practical to decode the CDMA channel codeusing full-complexity decoding techniques due to the largenumber of states. In this paper, we propose a suboptimalmaximum a posteriori (MAP) probability technique for de-coding the CDMA channel code, and the single-user codes aredecoded using full-complexity MAP probability algorithms, asdescribed originally by Bahlet al. [13].

We make the realization that the concatenation of twoconvolutional codes may be decoded in a Serial Turbo Code[14] fashion at the receiver. A feature of our system is thatthe convolutional code corresponding to the CDMA channelhas random generator polynomials. We do, however, havecontrol over the high-level statistics of the polynomials viathe spreading code length and the level of asynchronism inthe channel. The exploitation of this control is not studied inthis paper.

0090–6778/99$10.00 1999 IEEE

ALEXANDER et al.: ITERATIVE MULTIUSER INTERFERENCE REDUCTION: TURBO CDMA 1009

We are encouraged by the result of Jana and Wei [15] thatstates that the minimum distance of the single-user codes arenot compromised by the process of spreading and despreadingin a multiuser environment. Additionally, Douillardet al.[16] realized that the intersymbol interference (ISI) channelmay be viewed as a convolutional code and, therefore, wereable to view a system incorporating FEC as a concatenatedconvolutional code system. We make the same realization here,but with the CDMA channel substituted for the ISI channel.Indeed, the model of a CDMA channel is equivalent to themodel of an ISI channel where the taps of the ISI channelmodel are time varying.

Random spreading codes are explicitly considered sincethey allow for interferer diversity, which is not the case forfixed spreading codes. Asynchronous transmission is permittedto move complexity from the mobile terminal into the basestation. We assume a random-access system where the amountof coordination between base station and user is minimized.

This paper is organized as follows: in Section II, the con-volutional code model for the CDMA channel is describedwhere a noise-whitening matched filter is required. The de-coder for the serially concatenated convolutional transmittermodel is discussed in Section III and simulated in Section IV.Conclusions are given in Section V.

Throughout this paper, scalars are lowercase, vectors areunderlined lowercase, and matrixes are underlined uppercase.Subscripting is dropped when no ambiguities will arise. Thesymbols and are the transposition and inversionoperators, respectively. The delimiter defines a space ofdimension . Vector subscripting can be of the form ,denoting the th component of vector When is someconstant, then the subscript implies vector size, i.e., isa column vector of zeros of size . We shall use a notationfor subvectors, whereby the vector consisting of elementsthrough inclusive of vector , i.e, shallbe denoted .

II. CHANNEL MODEL

A well-known model for the -symbol, -user symbol-asynchronous CDMA channel employing spreading codes oflength is described presently. In particular, the output ofa filter matched to the common chip waveform employed byall users is

(1)

where describes the CDMA channel over which each of theusers transmits and is defined in terms of the spreading codesemployed by each user and the relative delays of the users’transmissions measured at the receiver.

where is the set of possible chipamplitudes. The channel symbol interval and

user index , are derived from the transmissionnumber as follows:

where is the smallest integer not less than. The spreadingcode , is of length chips and is employed by usertotransmitted bit . We have restricted consideration to the chipsynchronous case. The diagonal matrix contains, on thediagonal, the received amplitudes of each user’s waveform.The noise vector represents the sampled AWGN in thesystem. It has the property , where isthe variance of the noise process.

The binary code words of lengthgenerated by each of theusers’ encoders appear in the data vectoras follows:

(2)

Considering the fact that the elements ofresult fromsingle-user encoders of rate 1/, we have that bit ofsymbol transmitted by user is element

of . The transmission index may be formed as where

and is the collective number of channel bitstransmitted by the users. We shall place the informationsymbols of all users into the vector. The objective of thereceiver is to determine an estimate for this vector.

When the noise whitening matched filter is applied to,the resulting CDMA channel may be viewed as a real time-varying convolutional code. The encoder does not employmodulo-2 additions as is conventionally the case, but stillpossesses properties such as distance spectra and generatingpolynomials. The filter is the orthogonal basis resulting fromthe Gram–Schmidt orthogonalization of, i.e.,

where is lower triangular with bandwidth ,and has the same dimensions as. The number of memoryelements required in the convolutional encoder is one less thanthe bandwidth of the encoding matrix [17].

Note that an identical model results for the multipath fadingchannel case [18]. The output of the filter is

(3)

(4)

The statistics of the noise are preserved due to the orthogonalnature of the projection . Specifically, are independentlyidentically, distributed (i.i.d.) Gaussian with variance, i.e.,

. We may think of the columns of asmodifications of the conventional coded matched filters.In fact, , which states that the columns of arelinear combinations of the original spreading codes. Since

1010 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 7, JULY 1999

Fig. 1. Signal at receiver model.

is invertible for linearly independent columns of is asufficient statistic. The two key features ofthat distinguishit from the conventional matched filter statistic are:

1) the noise component in is white;2) the interference results from only other transmis-

sions rather than in the conventional case.

We can view the matrix as an encodingmatrix. The convolutional code described byproduces oneof 2 codewords for each input bit. Therefore, the code israte 1/ and has memory elements. In real time,the input and output symbol rates are identical, only thecardinality of the input and output alphabets are different.The generator polynomials, set by the CDMA channel, are,in general, time-varying due to the use of random spreadingcodes. The sequence observed by the receiver is modeled asshown in Fig. 1 where we have assumed each of the single-user encoders employ convolutional codes withmemoryelements each.

Observe the concept of an “inner code” and an “outercode” in the model. The outer code pertains to the single-user encoders and the inner code is the CDMA channel. Wehave not specified the details of the “outer code” since thereare several possibilities and the details are not important toour decoding system. The total number of memory elementsin the “outer code” is . One can place the informationsymbols from each of the users into a vectorand constructa generator matrix corresponding to a code withmemory elements where . The critical realizationis that it is correct to model the output of the “outer code”as a multiplexing of outputs of the single-user encodersaccording to (2). In summary, a valid abstraction of anasynchronous CDMA system with independent single-userencoding is a concatenated code where the constituent codesare convolutional codes with generators and . Withthis realization inhand, new techniques for decoding seriallyconcatenated codes may be employed.

Note that there are other filters that allow the CDMAchannel to be viewed as a convolutional code, i.e., the raw

channel of (1) is a convolutional code with varying-rateand binary coefficients. Although the overall rate of the codeis still 1/ , the number of bits consumed by the decoder variesaccording to the number spreading sequences that overlap inthe channel matrix . The more columns of that overlap,the more bits consumed by the encoder. The rate for the

channel realization is constant at 1/. We employ thechannel for reasons that allow effective complexity reductionin the decoder. Note that the receiver must derivewhichrequires knowledge of . The matrix is uniquely definedby the set of delays and the random spreadingcodes employed by the users.

Fig. 2. Receiver structure.

A joint decoder for this serially concatenated code wouldrequire a trellis with states. Note that this numberof states satisfies the following boundary conditions:

1) single-user: ;2) no coding:

We shall not attempt to find a suboptimal solution for theprohibitively large joint trellis. Rather, we focus on the seriallyconcatenated nature of the encoder. We shall assume that thesingle-user encoders interleave their output sequence at thecode word bit level to aid in the decoding process.

III. D ECODER

Due to the serially concatenated convolutional code struc-ture of the transmitter, we propose a Turbo code style decodingprinciple where the inner code creates reliability informationfor the outer code, which in turn creates reliability for the innercode. The iterative process continues until further iterationsyield minimal improvement. Thead hocnature of the systemis rooted in thead hocnature of Turbo codes. No criteria hasbeen given for the stability of what amounts to a nonlinearrecursive filter. Turbo codes have acquired notoriety, and weexplore their application to our abstraction of the CDMAcommunications system.

The receiver system diagram is shown in Fig. 2 where thepresence of interleaving blocks requires that, in the transmit-ter, the users interleave their encoder output streams beforetransmission across the CDMA channel. The interleaving isemployed to spread burst errors that arise in the single-userdecoders. In Fig. 2 we have shown the interleaving blocks asone device, although they consist of parallel devices. Thedecoder operates on the sequence. The soft output of theCDMA MAP decoder is

and is produced as follows:

(5)

where

(6)

and

(7)

ALEXANDER et al.: ITERATIVE MULTIUSER INTERFERENCE REDUCTION: TURBO CDMA 1011

We may think of the summation as averaging out the otherusers’ contributions, thus forming a probability for the user ofinterest. Defining the state of the CDMA encoder at symbolinterval to be , we seethat the summation in (6) is over all states on the CDMA trellisat symbol interval . Note that since the bandwidth ofis , the state has binary elements and thereforethere are states. The state probability can be computedusing Bahl’s method of forward and backward recursions [13]as follows:

(8)

(9)

The probability in (5) is thea priori information aboutthe symbol and at the first iteration is set to be 0.5 forboth and On subsequent executions of theCDMA MAP decoder, this probability will be furnished bythe single-user MAP decoders. The likelihoodis, from (4), Gaussian with variance

(10)where is the nonzero part of row of , i.e.,

The deinterleaver, with knowledge of the single-userdeinterleavers, implements one deinterleaving operation on thesoft output of the CDMA MAP decoder. Each user’s MAPdecoder produces both a soft output pertaining to its part of

and an estimate of its information sequence (the originalinput to its convolutional encoder). For user, the soft outputinformation is

(11)

The single-user MAP decoders operate identically to themethod proposed by Benedetto and Montorsi [14] for second-stage decoders in a serial Turbo decoder. This method isequivalent to the MAP algorithm of Bahlet al. [13] thatgenerates thea posteriori probabilities of the states and statetransitions at each time interval for a finite-state machine basedon noisy observations.

Here, we take the perspective that the input to the MAPdecoder is a sequence ofa priori likelihoods, say , for thesymbols on the trellis transitions . In this way, the transitionprobabilities of Bahlet al. are

(12)

where is the set of integers specifying the channelsymbols generated by the transition from stateto state

in symbol interval of user ’s encoder

In our development we provide thea priori likelihoods for thesymbols on the trellis transitions as

(13)

The algorithm of Bahlet al. is used to compute the stateprobabilities at each trellis interval. These are then employedin the construction of information symbol and channel symbola posteriori likelihoods. The MAX operation of the MAPalgorithm is then applied to make a decision on the informationsymbols by selecting the symbol with the highesta posteriorilikelihood. Central to the execution of our iterative algorithmis the collection of thea posteriorichannel symbol likelihoodsinto the reliability information . These are then collectedacross users as follows:

This information is interleaved for use in the next pass throughthe CDMA MAP decoder. The interleaving amounts to apermutation, according to the interleaver of user, of theindex in (11). The reliability information is employed bythe following assignment:

which is a priori information in (5). This process is identicalto the operation of a decoder for serial Turbo codes [14].

A. Approximate Solution

The trellis over which the CDMA MAP decoder operateshas states which is too large for even moderate numbersof users. We shall employ a method proposed by Mehlan andMeyr for the ISI channel [19] that was adapted to the CDMAcase1 by Alexander and Rasmussen [20]. This previous workneglected the option of iterating that has been realized in thispaper. Two approximations result in an approximate solutionthat is , instead of as for the full MAP decoderfor the CDMA channel.

The first approximation is justified by an observation madeby Wei and Schlegel [21]. Their results imply that analgorithm applied to the forward recursion in (8) will return,at time of the largest with very highprobability. The application of the algorithm to thechannel of (3) is pivotal. The sum of (6) is over allstates in the CDMA trellis. We shall replace this with a sumover states that are surviving paths in thealgorithm for theforward recursion and assume the other states have a negligiblecontribution.

(14)

where is the set of states surviving attime . This approximation impacts on the backward recursion.

1The CDMA channel is a time-varying ISI channel.

1012 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 7, JULY 1999

Fig. 3. Approximate MU CDMA MAP decoder step.

Specifically, we only require the that growfrom the states in .

The second approximation involves the backward recursionof (9). Again, following the development in [19] and [20], wecut the length recursion into recursions of depth two.There is little point reducing the complexity of the forwardrecursion if we still require a full computation of the backwardrecursion in order to compute the state probabilities. We couldallow the forward recursion to execute then compute therequired probabilities from the backward recursion. Given thatwe would like to use state probabilities to steer the forwardrecursion, we require results from both backward and forwardrecursions. Specifically we set

(15)

where it is apparent that we have set the initial conditionfor each of the four recursions to 1/4. The

bits and are set by the summations and bitsthrough are set by the surviving state from theforward recursion, i.e., an element of . This approximationis equivalent to assuming that the distant future values of

have minimal effect on the current value eventhough they are involved in the recursion of (8). Specifically,we have assigned a uniform distribution toof which there are four candidates due to the possible valuesof the 2-tuple .

A graphical view of a step in the CDMA trellis is shownin Fig. 3. The binary tree of depth three is grown from eachof the surviving paths in the forward recursion at time .The new transitions pertain to channel symbols , and

. The extension to symbol creates nodes. For eachof these nodes, the approximate backward recursion is

computed using symbol intervals and The jointlikelihood is then computed for each of thenodes using (7). Equations (5) and (6) are then implementedfor and to produce the required likelihoods

The of node selection process retains thenodes with largest

In the original work of Mehlan and Meyr [19], the depth ofthe backward approximation was one. With this depth look-ahead, a high level of noise in the look-ahead bit interval cansteer the algorithm off course. In our case we chose thelook-ahead depth to be two in order to reduce the likelihoodof such occurrences. Although higher depth look-aheads maybe employed, the complexity of the system increases expo-nentially with the depth. As the complexity of the algorithmincreases exponentially with the look-ahead depth, we do notconsider depth three or more.

B. Complexity

As can be seen from Fig. 3 there are 14 conditional probabil-ities, of the form shown in (10), to be computed for the growthof each of the surviving nodes. Using the number of suchprobability computations as the measure of complexity, wecan show that the full complexity MU MAP requires persymbol interval, whereas the proposed scheme requires only

As will be shown, it is reasonable to set in orderto achieve similar performance and, hence, our algorithm hascomplexity

IV. SIMULATION

In this section, we present the performance of the proposedsystem. The ratio of the number of usersto the spreadingcode length (or processing gain) is kept high for goodspectral efficiency. The error control codes employed by theusers were simple rate 1/2, four-state convolutional codeswith generators If a more powerful code wasemployed, the single-user performance would improve and itis our expectation that the multiuser receiver proposed herewould follow this improvement. We do not terminate theconvolutional code trellis.

Since the system is aimed at packet radio systems, theusers encode blocks of length The chipsconstituting each user’s binary spreading code are chosenrandomly and independently across user chip numberand symbol interval

We first simulate the system which allowsexecution of the full-complexity MU MAP algorithm. With

the MU trellis has 16 states. The performance for full-complexity forward recursion and full-complexitybackward recursion is shown in Fig. 4 (FC 5/7) along withthe approximate reduced complexity method with(SO 5/7). With there are 16 states in the full trellis.In both cases, results are shown for iterations sinceno perceivable performance improvement was obtained bysubsequent iteration.

Ideally, the performance of a multiuser receiver should beindependent of the number of users so that quality-of-servicecan be guaranteed on a per user basis. This is not true as can

ALEXANDER et al.: ITERATIVE MULTIUSER INTERFERENCE REDUCTION: TURBO CDMA 1013

Fig. 4. Simulated system performance for(K = 5; N = 7) and(K = 10;N = 15):

be seen in Fig. 4 where plots for both (SU) andare shown. The effect of increasing the number of users from1 to 5 is equivalent to reducing the power of each user by0.5 dB. This loss is small compared with all other knownlinear systems that employ random codes or, equivalently,allow symbol asynchronism.

The full complexity MU MAP could not be executed forsince the trellis has 512 states. As can be seen in Fig. 4

(SO 10/15), the approximate solution of the MU MAP withprovides performance within 1 dB of the performance

of the system in the absence of multiuser interference. Theperformance improvement of our system over the case wherethe MU CDMA trellis is decoded using a linear method [6](Linear 10/15) is several decibels.

V. CONCLUSION

In this paper, we have proposed a multiuser receiver for thehighly loaded asynchronous CDMA channel where each userencodes their data before transmission. The operation of thereceiver is equivalent to a serial Turbo decoder in a single-user scenario. One of the decoders is for the CDMA channelwhich we view as a convolutional code and the other is forthe single-user encoders. A suboptimal method was proposedthat achieves performance remarkably close to single-userperformance with complexity that is linear in the number ofusers. The number of users is set to be a large fraction of theprocessing gain in order to achieve good spectral efficiency.The results obtained in this work also indicate that there isno need to decode all of the users jointly in one large trellis.A reduced complexity solution for the multiuser trellis thatoutperforms the current proposal remains to be found.

It is important to question the impact of spectrally efficientCDMA, where approaches on intercell interference in acellular CDMA communications network. For the IS-95 [4]case, where no attempt is made to remove the impact ofintercell users, the question had been addressed [22]. In [23],Newsonet al.show that for propagation loss exponent four and

shadowing variance 8 dB, half of the interference power at theoutput of a user’s correlator comes from intracell users, andthe other half comes from all other cells in the network. Theproposed scheme is still valid when the channels are multipathfading, provided the multipath channels can be tracked tosufficient accuracy. Any error in the channel estimates willmanifest as a noise floor in the error rate performance of thesystem. In this paper, we have described a receiver systemthat removes the intracell half of the interference power. Thisamounts to a 3-dB improvement, in terms of power controlsetpoint, with respect to conventional CDMA. Equivalently,twice as many users can now be supported as compared toconventional CDMA.

Further improvement can be obtained if the users at thefringe of the nearby cells are incorporated in the detectionprocess in the base station of interest. In this way the power ofthe interfering users is removed from the intercell interferencepower. Note that since these users would be in a soft-handoverstate for IS-95, the infrastructure required is already in place.

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Paul D. Alexander (S’92–M’96) received the B.E.and M.Eng.Sc. degrees from the University of Ade-laide, South Australia, in 1991 and 1995, respec-tively. He graduated with the Ph.D. degree and adissertation called “Coded Multiuser CDMA,” inMarch 1997 from the University of South Australia.

From April 1996 to August 1997, he was thePost-Doctoral Fellow in the Mobile Communica-tions Research Center at the University of SouthAustralia working on mobile broadband systemsincorporating CDMA. Since August 1997, he has

been involved in a smart antenna project for wideband CDMA at the Centerfor Wireless Communications at the National University of Singapore. Hisresearch interests include multiuser communication theory in general andmultiuser CDMA systems specifically.

Mark C. Reed (M’95) was born in Geelong,Australia, on November 20, 1967. He receivedthe degree in electronic engineering (with honors)from the Royal Melbourne Institute of Technologyin 1990.

He worked in industry for five years designingdigital hardware, real-time software, and modemsfor the public switched telephone network. InSeptember 1995, he joined the Mobile Commu-nication Research Center at the University ofSouth Australia, where he is currently pursuing the

Ph.D. degree, with a thesis called “Turbo Coding Applications for PersonalCommunication Systems.” His areas of interest include coding techniques,multiuser receiver design, and more generally mobile radio systems.

John A. Asenstorfer (M’96) received the B.Sc.,B.MSc., and B.Eng. degrees from the Universityof Adelaide, and the M.Eng. degree in 1987 fromthe University of South Australia, while with theDigital Communications Group. He graduated withthe Ph.D. degree in 1995 from the University ofAdelaide.

He currently directs research in mobile com-munications at the Institute for TelecommunicationResearch at the University of South Australia, wherehe is with the Information Technology Faculty. His

interests are in the area of signal processing, wireless communications, andmultiple-access communication. He has wide experience in national andmultinational projects, collaborating with industrial and academic partners.

Dr. Asenstorfer is a member of the IEEE Information Theory, SignalProcessing, and Communications Societies.

Christian B. Schlegel (S’86–M’88–SM’97) wasborn in St. Gallen, Switzerland, on August 22,1959. He received the Dipl.-EI.-Ing. ETH from theFederal Institute of Technology, Z¨urich, Switzer-land, in 1984, and the M.S. and Ph.D. degreesin electrical engineering from the University ofNotre Dame, Notre Dame, IN, in 1986 and 1988,respectively.

In 1988, he joined the Communications Groupat the research center of Asea Brown Boveri, Ltd.,Baden, Switzerland, where he was involved in mo-

bile communications research. He spent the 1991–1992 academic year asa Visiting Assistant Professor at the University of Hawaii at Manoa, HI,before joining the Digital Communications Group at the University ofSouth Australia, Adelaide, Australia, where he supervised research in mobilecommunications. In 1994, he joined the University of Texas at San Antonio.He is currently with the Department of Electrical Engineering, University ofUtah, Salt Lake City. His interests are in the area of digital communications,coded modulation, mobile radio, and multiple-access communication. Herecently completed the research monographTrellis Coding (Piscataway, NJ:IEEE Press, 1997) and is currently working on a book entitledCoordinatedMultiple User Communications, jointly with Dr. Alex Grant. His work iswidely published and he consults for and cooperates with diverse nationaland international industrial and academic partners.

Dr. Schlegel is a member of the IEEE Information Theory and Commu-nications Societies.